Could you please demonstrate Brewster's angle and Critical angle in equation form and how to solve for it. still don't understand. Thank you

Part A) A solid sphere of mass M and radius R is mounted on an axle through its center. The axle is attached to a horizontal spring of constant k, and the sphere rolls back and forth without slipping. Derive an expression for the total energy of this system in terms of the displacement of the spring x, speed v of the center-of-mass of the sphere when its displacement is x, and M, and k.

Part B) Derive the expression for the angular velocity of the oscillation. Hint: Take the derivative of the energy with respect to time and set it equal to zero. The acceleration of simple harmonix motion is of the form alpha = -omega^(2) * x

(For part A I used 2/5MR^2 for the moment of inertia but it is saying it is wrong so please help)

Two capacitors,

C₁ = 16.0 μF

and

C₂ = 32.0 μF,

are connected in series, and a 15.0-V battery is connected across them.

(a) Find the equivalent capacitance, and the energy contained in this equivalent capacitor.

(b) Find the energy stored in each individual capacitor.

(c) If the same capacitors were connected in parallel, what potential difference would be required across them so that the combination stores the same energy as in part (a)?
V____

Which capacitor stores more energy in this situation, C₁ or C₂?

C₁C₂    Both C₁ and C₂ store the same amount of energy.

A laser used in LASIK eye surgery produces 55 pulses per second. The wavelength is 193 nm (in air), and each pulse lasts 10.0 ps. The average power emitted by the laser is 120.0 mW and the beam diameter is 0.80 mm.

(a) What is the total energy of a single pulse? mJ

(b) What is the intensity during a pulse? W/m2

Describe what a periodic phenomenon is,and what is Period and frequency.

7. A farsighted man uses eyeglasses with a refractive power of 2.00 diopters. Wearing the glasses 0.020 m from his eyes, he is able to read books held no closer than 0.304 m from his eyes. He would like a prescription for contact lenses to serve the same purpose. What is the correct contact lens prescription, in diopters?
diopters

A 1270-kg cannon shoots a 34.3-kg shell at an angle of 24.7° above the horizontal and a speed of 491 m/s. What is the recoil velocity of the cannon?

19.0-L tank of carbon dioxide gas (CO2) is at a pressure of 9.40 ✕ 105 Pa and temperature of 18.0°C. (a) Calculate the temperature of the gas in Kelvin. K (b) Use the ideal gas law to calculate the number of moles of gas in the tank. mol (c) Use the periodic table to compute the molecular weight of carbon dioxide, expressing it in grams per mole. g/mol (d) Obtain the number of grams of carbon dioxide in the tank. g (e) A fire breaks out, raising the ambient temperature by 224.0 K while 82.0 g of gas leak out of the tank. Calculate the new temperature and the number of moles of gas remaining in the tank. temperature K number of moles mol (f) Using the ideal gas law, find a symbolic expression for the final pressure, neglecting the change in volume of the tank. (Use the following as necessary: ni, the initial number of moles; nf, the final number of moles; Ti, the initial temperature; Tf, the final temperature; and Pi, the initial pressure.) Pf = (g) Calculate the final pressure in the tank as a result of the fire and leakage. Pa

How dangerous is radioactivity? Discuss the real and imagined dangers. Give examples, along with numbers. Which risks are known from direct observation, and which are known only from calculations? What assumptions are made in calculating risk?

a) What is the relation between incline angle (0 degrees being flat, and 90 degrees being a vertical incline) and acceleration along the incline when friction is not involved?

g*(1-cos(theta)^2); g*sin(theta); g*(1-cos(theta)) or g*cos(theta)

b) When an object is on an incline, what is the relation between the objects weight and the normal force?

m*g*cos(theta); m*g*sin(theta); m*g*(1-cos(theta)) or m*g*(1-cos(theta)^2)

c) What is the force required to make an object under static friction begin motion?

a. the normal force times the coefficient of static friction

b. the normal force times the coefficient of kinetic friction

c. the force due to gravity times the coefficient of kinetic friction

d. mass times the coefficient of static friction

d) What is the relation between the coefficient of kinetic friction and the angle of inclination required to make an object have a constant velocity (no acceleration) going down an incline?

g*m*cos(theta); g*m*cos(theta) - N; tan(theta) or g*(1-cos(theta)^2)

e) The small angle approximation states that sin(theta) can be approximated as what when the angle, theta, is small?

theta in degrees; 1 - theta in radians; 1; or theta in radians

You have a 200 Ω resistor, a 0.400-H inductor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0V and an angular frequency of 250 rad/s.

Parts A, B, C
For this R-L circuit graph v, vR, and vL versus t for t = 0 to t = 50.0 ms. The current is given by i=Icosωt, so v=Vcos(ωt+ϕ).

Part D
What are v, vR, and vL at t = 20.0ms?
Enter your answers numerically separated by commas.

v,vR,vL v , v R , v L = ?, ?, ? V

Part F
What are v, vR, and vL at t = 40.0ms?
Enter your answers numerically separated by commas.

v,vR,vL v , v R , v L = ?, ?, ? V

a ferris wheel 42.5m in diameter rotates once every 18.2s. What is the ratio of a person's apparent weight to her real weight at (a) the top and (b) the bottom?

please please PLEASE show all steps and write out all the work I have been stuck on this problem and I can't figure out where I'm going wrong.

Do all objects in free fall reach terminal velocity because I thought objects in free fall always accelerate with 9.8 m/s/s so why is there a point where they stop accelerating

A 7.50g bullet traveling at 490m/s embeds itself in a 1.59kg wooden block at rest on a frictionless surface. The block is attached to a spring with k = 89.0N/m

Find the Period

Find the amplitude of the subsequent simple harmonic motion.

A 22 g ball with a radius of 29 mm rolls back and forth in a hemispherical bowl of radius 6 cm.

(a) What is the period of the oscillation if the ball is solid?


(b) What is the period of the oscillation if the ball is hollow?


(c) What is the percent difference between the two?